MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation Articles uri icon


  • Rodrigues, Miguel R. D.
  • VERDU, S.

publication date

  • March 2010

start page

  • 1070

end page

  • 1084


  • 3


  • 56

International Standard Serial Number (ISSN)

  • 0018-9448

Electronic International Standard Serial Number (EISSN)

  • 1557-9654


  • In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input-multiple-output (MIMO) Gaussian channels with arbitrary
    input distributions, by capitalizing on the relationship between mutual
    information and minimum mean-square error (MMSE). The optimal linear
    precoder satisfies a fixed-point equation as a function of the channel
    and the input constellation. For non-Gaussian inputs, a nondiagonal
    precoding matrix in general increases the information transmission rate,
    even for parallel noninteracting channels. Whenever precoding is
    precluded, the optimal power allocation policy also satisfies a
    fixed-point equation; we put forth a generalization of the
    mercury/waterfilling algorithm, previously proposed for parallel
    noninterfering channels, in which the mercury level accounts not only
    for the non-Gaussian input distributions, but also for the interference
    among inputs.